The sum of two angles is $84^\circ$. Angle 2 is $156^\circ$ smaller than $4$ times angle 1. What are the measures of the two angles in degrees?
Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 84}$ ${y = 4x-156}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${4x-156}$ for $y$ in the first equation. ${x + }{(4x-156)}{= 84}$ Simplify and solve for $x$ $ x+4x - 156 = 84 $ $ 5x-156 = 84 $ $ 5x = 240 $ $ x = \dfrac{240}{5} $ ${x = 48}$ Now that you know ${x = 48}$ , plug it back into $ {y = 4x-156}$ to find $y$ ${y = 4}{(48)}{ - 156}$ $y = 192 - 156$ ${y = 36}$ You can also plug ${x = 48}$ into $ {x+y = 84}$ and get the same answer for $y$ ${(48)}{ + y = 84}$ ${y = 36}$ The measure of angle 1 is $48^\circ$ and the measure of angle 2 is $36^\circ$.